The inside diameter of a randomly selected piston ring is a random variable with

Question

The inside diameter of a randomly selected piston ring is a random variable with mean value 8 cm astandard deviation 0.07 cm (a) If Xis the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X distribution? (Enter your standard deviation to five decimal places center standard deviation cm cm (b) Answer the questions posed in part (a) for a sample size of n = 64 rings. (Enter your standard deviation to five decimal places.) center standard deviation cm cm (c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 0.01 cm of 8 cm? Explain your reasoning O X is more likely to be within 0.01 cm of 8 cm in sample (b) because of the decreased variability with a larger sample size O X is more likely to be within 0.01 cm of 8 cm in sample (a) because of the decreased variability with a smaller O X is more likely to be within 0.01 cm of 8 cm in sample (a) because of the increased variability with a smaller O X is more likely to be within 0.01 cm of 8 cm in sample (b) because of the increased variability with a larger sample size sample size sample size

Explanation / Answer

mean is 8 and s is 0.07

a) for sample size of 16, the standard error SE=s/sqrt(N)=0.07/sqrt(16)=0.0175

thus center is 8 and standard deviation for sample is 0.0175

b) for sample size of 64, the standard error SE=s/sqrt(N)=0.07/sqrt(64)=0.00875

thus center is 8 and standard deviation for sample is 0.00875

c) answer is A

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